"Liana" wrote in message <inb54p$lpc$1@fred.mathworks.com>...
> Thanks, Roger. Let me just clarify one more thing: in my case P1 is a point [10 10 10]. so, is it enough just to check if dot(normal,P4-P1) and dot(normal,P5-P1) have opposite sign?
- - - - - - - - -
Yes, it is sufficient. The respective values of dot(normal,P4-P1) and dot(normal,P5-P1) are unchanged if you replace P1 with P2 or P3, because all three points lie in the plane.

Roger Stafford

Subject:Intersection of a plane and finite line segment in 3D spaceFrom:Liana

I suppose that I missed one thing: P1 = [10 10 10] Do these numbers correspond to x,y and z coordinates of the same point or do they correspond to 'x' coordinates of three points? As far as I understand the second variant is correct. (?)

"Roger Stafford" wrote in message <inb6ho$d0e$1@fred.mathworks.com>...
> "Liana" wrote in message <inb54p$lpc$1@fred.mathworks.com>...
> > Thanks, Roger. Let me just clarify one more thing: in my case P1 is a point [10 10 10]. so, is it enough just to check if dot(normal,P4-P1) and dot(normal,P5-P1) have opposite sign?
> - - - - - - - - -
> Yes, it is sufficient. The respective values of dot(normal,P4-P1) and dot(normal,P5-P1) are unchanged if you replace P1 with P2 or P3, because all three points lie in the plane.
>
> Roger Stafford

Subject:Intersection of a plane and finite line segment in 3D spaceFrom:Liana

It means that the line intersects the plane, however it doesn't. Where is my error?

"Roger Stafford" wrote in message <inb6ho$d0e$1@fred.mathworks.com>...
> "Liana" wrote in message <inb54p$lpc$1@fred.mathworks.com>...
> > Thanks, Roger. Let me just clarify one more thing: in my case P1 is a point [10 10 10]. so, is it enough just to check if dot(normal,P4-P1) and dot(normal,P5-P1) have opposite sign?
> - - - - - - - - -
> Yes, it is sufficient. The respective values of dot(normal,P4-P1) and dot(normal,P5-P1) are unchanged if you replace P1 with P2 or P3, because all three points lie in the plane.
>
> Roger Stafford

Subject:Intersection of a plane and finite line segment in 3D spaceFrom:Liana

I'm sorry, I should paraphrase my question. What I'm searching is the intersection of the line segment and the triangle (not tetrahedron) in 3D space. I think that's the reason why I get incorrect results. In fact, the triangle belongs to the plane, but it is just a fragment of that plane. Does anybody know how to update my code to determine such intersection? Thanks a lot for any suggestion.

On Apr 4, 8:54 am, "Liana " <liananapalk...@email.arizona.edu> wrote:
> I'm sorry, I should paraphrase my question. What I'm searching is the intersection of the line segment and the triangle (not tetrahedron) in 3D space. I think that's the reason why I get incorrect results. In fact, the triangle belongs to the plane, but it is just a fragment of that plane.

1) Find the intersection point p between the line L and
the plane P, if such a point exists
2) Determine if p belongs to the finite section of L
3) Determine if p is located in the interior of the
triangle T, given by the points (q,r,s).

Rune

Subject:Intersection of a plane and finite line segment in 3D spaceFrom:Liana

Thanks, Rune. Another solution could be the following: 1) check if the ray intersects the triangle, and 2) in case of intersection, check if the intersection point belongs to the line segment defined by two points in 3D.

Rune Allnor <allnor@tele.ntnu.no> wrote in message <70a9d01e-e1bb-47da-83f6-5dc20ab2d44a@dr5g2000vbb.googlegroups.com>...
> On Apr 4, 8:54 am, "Liana " <liananapalk...@email.arizona.edu> wrote:
> > I'm sorry, I should paraphrase my question. What I'm searching is the intersection of the line segment and the triangle (not tetrahedron) in 3D space. I think that's the reason why I get incorrect results. In fact, the triangle belongs to the plane, but it is just a fragment of that plane.
>
> 1) Find the intersection point p between the line L and
> the plane P, if such a point exists
> 2) Determine if p belongs to the finite section of L
> 3) Determine if p is located in the interior of the
> triangle T, given by the points (q,r,s).
>
> Rune

Subject:Intersection of a plane and finite line segment in 3D spaceFrom:Rune AllnorDate: 4 Apr, 2011 08:29:26Message: 10 of 10

On Apr 4, 10:16 am, "Liana " <liananapalk...@email.arizona.edu> wrote:
> Thanks, Rune. Another solution could be the following: 1) check if the ray intersects the triangle, and 2) in case of intersection, check if the intersection point belongs to the line segment defined by two points in 3D.

Well - not really.

The procedure I stated does the least amount of computations
necessary before each check. If you are a little bit careful
about how you state the problem, my method wastes only a small
number of computations in case p is outside the relevant interval
of L. If it is, there is no point in doing all the computations
required to determine if p is inside T.

With your suggestion one would need to do all the computations
every time. Might be a lot slower, depending on the application.

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